Despite the recognition that reflection is an essential part of problem solving, it is often not emphasized in upper-division physics courses. In this paper, we discuss homework corrections (HWCs) as a pedagogical tool to motivate reflection on homework assignments. We focus on gaining a qualitative understanding of how students may engage with the process of homework corrections, considering potential impacts on content understanding, metacognitive skills, and affect. To do so, we present three comparative case studies to elucidate different aspects of student engagement with HWCs; we also present descriptive statistics of participation in HWCs. We find that HWCs can be a useful pedagogical tool, but more scaffolding may be necessary to support students in identifying and learning from their mistakes, even in upper-division courses.